In the last few years, macroeconomists and industrial organization
researchers have reexamined relationships among scale economies,
markups, economic profitability and productivity growth. Paul Romer |14~
has emphasized the importance of increasing returns for productivity
growth at the aggregate industry or economy level. Empirical evidence
supporting this at the industry level has been presented by Robert Hall |4;5~, who reported both significant increasing returns and markups of
price over marginal cost in various U.S. manufacturing sectors. Related
evidence on the cyclical nature of markups in these industries,
suggesting some procyclicality of markup behavior, has been presented by
Domowitz, Hubbard and Petersen |3~.

Analysis of the cyclical characteristics of Robert Solow's |16~
productivity residual provided the basis for these empirical studies.
The resulting framework is limited, however, by its dependence on a
number of restrictive assumptions, which severely hamper analysis of
interactions among these characteristics. The purpose of this paper is
to extend this type of analysis to consider profit-maximizing markups,
economic profitability, scale economies, capacity utilization and
productivity growth within an integrated theoretical structural model,
and to assess their interactions empirically for two-digit U.S.
manufacturing data.

More specifically, using the "new industrial economics"
approach outlined by Timothy Bresnahan |2~ in which marginal cost and
therefore markups are unobserved but estimated econometrically, I
specify an integrated cost and demand structure for each industry. The
structure is quite general in that (i) markups and returns to scale are
permitted to vary over time (they are not constant parameters); (ii)
short- and long-run impacts are distinguished (by explicit recognition
of adjustment costs); (iii) quasi-fixity of both capital and labor is
incorporated (to accommodate labor hoarding as well as slow adjustment
of capital); (iv) input substitution is not constrained a priori (a
generalized Leontief restricted cost function based on gross output is
employed); (v) nonstatic expectations are allowed for (through an
instrumental variable estimation procedure); and (vi) the effects of
cost and demand "shocks" are directly represented (by
specifying and estimating industry-specific cost, output demand and
input demand functions).

Measures of technological and market factors affecting productive and
financial performance such as scale economies, utilization and markups
by industry are of interest in their own right. However, this general
specification not only allows such measures to be computed, but also
permits their linkages and their impacts on productivity growth and
economic profitability--both secular and cyclical--to be formalized and
measured. This is accomplished through analysis of "error
biases" that result when using traditional primal multifactor
productivity growth measures that fail to take into account the effects
of these factors. This facilitates assessment of conjectures such as
that by Hall |5~, that evidence of normal economic profits and markups
of price over marginal cost in most U.S. manufacturing industries imply
substantial scale economies and excess capacity.

The impact of these factors affecting economic performance is
measured by estimating structural equations representing input demand
and pricing behavior for seventeen 2-digit U.S. manufacturing
industries, and aggregated total manufacturing. The data used are annual
data from 1949 to 1986 from the Bureau of Labor Statistics on prices and
quantities of gross output, and capital, labor, intermediate material,
energy and purchased services inputs. The principal empirical findings
are that markups have been countercyclical and have an upward trend for
most industries, and that excess capacity and the potential to exploit
scale economies have tended to expand over time. These factors have
caused standard measures of productive performance to overstate the
degree of fluctuation and downturn in productivity growth in most U.S.
manufacturing industries. In addition, in terms of financial
performance, these characteristics of cost and demand tend to offset
each other, resulting in approximately normal profits on average,
although declining profitability since 1973 is apparent for a number of
industries.

II. Modeling Economic Performance and Its Determinants

Fundamental Results Used for the Analysis

To motivate formally the theoretical linkages among productivity
growth, markups, scale economies and capacity utilization, I will rely
primarily on three results. These results can be combined and employed
directly to motivate the use of estimated cost and demand elasticities
to measure these factors, and to generalize, refine and interpret
productivity growth and profitability measures.

First, I will use the traditional output-side specification of the
productivity growth residual motivated by Solow |16~ (the Solow
residual):

|Mathematical Expression Omitted~,

where Y and |p.sub.Y~ are output quantity and price, |v.sub.j~ and
|p.sub.j~ are corresponding input measures, "|center dot~"
denotes a time derivative, t represents time and |S.sub.j~ is the
revenue share |p.sub.j~|v.sub.j~/|p.sub.Y~Y. This expression,
representing the growth in output that cannot be attributed to growth in
inputs--technical change, is based on manipulation of the production
function Y = Y(v, t).

With perfect competition, instantaneous adjustment (full utilization)
and constant returns to scale (CRTS), this is equivalent (with a sign
change) to the cost-side specification capturing the diminution of costs
not explained by changes in input prices and derived from the cost
function C(Y,p, t):(1)

|Mathematical Expression Omitted~,

where C is total costs and |M.sub.j~ is the cost-share
|p.sub.j~|v.sub.j~/C.

Secondly, I will exploit information on the deviation between costs
(C) and revenues (|p.sub.Y~Y) due to violation of the assumptions used
to motivate the equivalence of (1a) and (1b). This can arise due to
imperfect competition (implying |p.sub.Y~ |is not equal to~ MC, where MC
= |Delta~C/|Delta~Y represents marginal cost), or to nonconstant returns
to scale or fixity (resulting in AC |is not equal to~ MC, where AC |is
equivalent to~ C/Y denotes average cost).(2) As shown elsewhere |10~,
recognizing these differences results in the relation

Thirdly, a result based on the ||Epsilon~.sub.CY~ elasticity can be
used to interpret equation (2) further: |Delta~ ln C/|Delta~ ln Y =
(|Delta~C/|Delta~Y)Y/C = MC/AC differs from one if either nonconstant
returns (long run fixities) or short run fixities exist. Specifically,
as shown in Morrison |10~, ||Epsilon~.sub.CY~ can be defined as:

|Mathematical Expression Omitted~,

where |Mathematical Expression Omitted~ is (the inverse of) returns
to scale, L denotes long run, and C|U.sub.c~ is a cost-side measure of
capacity utilization.

Putting the second and third results together leads to |Mathematical
Expression Omitted~. An important implication of this expression is that
when ADJ |is not equal to~ 1 due to ||Epsilon~.sub.PY~ |is not equal to~
0 from product differentiation or ||Epsilon~.sub.CY~ |is not equal to~ 1
from either scale economies or fixity, the equivalence of (1a) and (1b)
is destroyed. Incorporating this information thus requires correcting
the ||Epsilon~.sub.Ct~ and ||Epsilon~.sub.Yt~ measures, which in turn
has implications for decomposing ||Epsilon~.sub.Yt~ to identify the
impacts of the underlying technical and market factors on overall
productivity growth or productive performance. In addition, the
deviation between |p.sub.Y~Y and C has important implications about
financial performance, since if |p.sub.Y~ Y/C = 1 (ADJ = 1) normal
profits will be observed. This provides a useful context in which to
assess the Hall |5~ contention that capacity utilization and returns to
scale may attenuate the profitability arising from market power. In
essence this implies that ||Epsilon~.sub.CY~ counteracts |p.sub.Y~/MC,
which could potentially occur with excess capacity (so
||Epsilon~.sub.CY~ |is less than~ 1), and markups (so |p.sub.Y~/MC |is
greater than~ 1).

If normal profits are observed, this not only suggests that the
levels of the markup, capacity utilization and scale economies are such
that this condition holds, but also that if ||Epsilon~.sub.CY~ declines
(due either to decreases in capacity utilization or increases in
potential returns to scale), this will support a larger markup without
increasing overall profitability. In terms of the cyclical behavior of
markups, this suggests for example that (with CRTS) increases in
capacity utilization will be associated with decreases in markups;
markups will be countercyclical.(4)

These issues thus have important implications for the correct
measurement and interpretation of productive and financial performance.
To pursue these implications further, however, the necessary adaptations
of traditional productivity growth measures for these characteristics
must be formalized, and an empirically implementable model must be
developed to allow estimation of the appropriate elasticities. These
steps are pursued in the next two sections.

The Implications of These Relationships for Productivity Growth

Recognizing the impacts of markups, scale and fixity has somewhat
varied implications for productivity growth measurement. Correcting for
imperfect competition requires recognizing that the denominators of the
revenue and cost shares differ due to |p.sub.Y~ |is not equal to~ MC,
which necessitates an error bias correction to change the input
share-weights in the primal measure. Correcting for scale economies
requires accommodating a deviation between MC and AC; this implies an
error bias correction to change the denominator of the weights on both
output and input changes in the cost measure. Allowing for fixities
requires one more step; the numerator of both the primal and cost
share-weights for the fixed inputs as well as the denominator of the
cost shares must be adapted.

If scale economies or changes in capacity utilization also exist, the
assumption that ||Epsilon~.sub.CY~ = 1 must also be relaxed. To correct
for error biases arising from ||Epsilon~.sub.CY~ |is not equal to~ 1, it
must be recognized that (1b) is based on the assumption that the cost
function can be written as C(p, Y, t) = Yc(p, t) (where c = C/Y), so d
ln c/dt = d ln C/dt - d ln Y/dt. However, if ||Epsilon~.sub.CY~ |is not
equal to~ 1, this average cost derivative becomes d ln C/dt -
||Epsilon~.sub.CY~ (d ln Y/dt). Thus, to correct for ||Epsilon~.sub.CY~
|is not equal to~ 1 owing to scale economies, the residual
||Epsilon~.sub.Ct~ must be adjusted to

|Mathematical Expression Omitted~

where R represents "adjusted for returns to scale", and the
last term is the error bias in traditional measures when CRTS is assumed
inappropriately. Since ||Epsilon~.sub.CY~ = MC |center dot~ Y/C = MC
|center dot~ Y/AC |center dot~ Y = MC/AC, the adjustment by
||Epsilon~.sub.CY~ restates the change in output in terms of its correct
marginal value. The impact of the bias depends on the extent of scale
economies and the output growth rate.

If instead ||Epsilon~.sub.CY~ |is not equal to~ 1 because C|U.sub.c~
|is not equal to~ 1 ((1 - |Sigma~||Epsilon~.sub.Ck~) |is not equal to~
1), the correction requires changing the assumption that
|Delta~C/|Delta~|p.sub.j~ = |v.sub.j~ (the cost-minimizing demand for
input j) by Shephard's lemma, to recognize that the implied
equality of the value of the marginal product and input price is invalid for fixed inputs. The quasi-fixed inputs should therefore be valued in
terms of their shadow prices, |Z.sub.k~ (reflecting the true marginal
product of |x.sub.k~), instead of the market price |p.sub.k~, and input
shares should be measured in terms of C*. This implies an adjustment in
the numerator of the share weight on quasi-fixed input changes as well
as in the denominator for the weights of all inputs and output.

where F represents "adjusted for fixity". As above, the
last term in this expression can be thought of as an error bias, which
in this case depends on the relative growth rates of output and the
quasi-fixed inputs.

Once these corrections for the invalid assumptions of CRTS and
instantaneous adjustment are made, the independent impacts of scale and
utilization changes on productivity growth measures can be identified in
terms of a decomposition of the primal measure to reflect the different
cost impacts. This decomposition is analogous to the treatment of
returns to scale motivated by Ohta |12~; the relationship between the
||Epsilon~.sub.Yt~ and ||Epsilon~.sub.Ct~ measures when
||Epsilon~.sub.CY~ |is not equal to~ 1 is |Mathematical Expression
Omitted~. This "decomposition" isolates technical change
independently from the characteristics captured in the deviation of
||Epsilon~.sub.CY~ from one, since it separately identifies the
different characteristics that cause ADJ |is not equal to~ 1. It
therefore facilitates interpretation by distinguishing the various
impacts causing fluctuations in the overall productivity growth measure
||Epsilon~.sub.Yt~.

III. Empirical Evidence on Markups, Fixities and Economic Performance

The Estimating Model

In order to implement and evaluate the productivity growth framework
developed in the last section, a model is required to separately
identify and measure the components of the ADJ measure--the elasticities
||Epsilon~.sub.PY~, |Mathematical Expression Omitted~, and
||Epsilon~.sub.Ck~. The approaches used by Hall |4~, and Domowitz,
Hubbard and Peterson |3~ cannot be used to carry out this task, since
they rely on an incomplete specification of the underlying cost and
demand relations. Instead, a more comprehensive specification employing
a production theory approach based on estimation of cost and demand
functions such as that developed in Morrison |6~ must be used for this
purpose.

The building blocks of this structural model, which provides the
basis for the estimated elasticities used below, are a Generalized
Leontief restricted cost function and a similarly constructed output
demand function. The specification used here assumes capital (K) and
labor (L) are quasi-fixed, energy (E), intermediate materials (M), and
purchased services (S) are the variable inputs, and adjustment costs are
accommodated by including investment in K and L (|Delta~K and |Delta~L)
as arguments of the cost function. The shift variables for the output
demand function include consumption expenditures, price indexes for
imported and consumption goods, the interest rate, and unemployment.

These two functions were used to construct a system of estimating
equations including (i) the cost function plus variable input demand
equations for E, M and S derived from Shephard's Lemma (|v.sub.j~ =
|Delta~C/|Delta~|p.sub.j~); (ii) a short run price setting equation MR =
MC using the expressions for marginal revenue (MR = |p.sub.Y~ +
(|Delta~|p.sub.Y~/|Delta~Y) |center dot~ Y) and marginal cost (MC =
|Delta~G/|Delta~Y); (iii) two Euler equations to reflect adjustment
paths of K and L; and, to complete the system, (iv) the output demand
equation.(6) The estimating equations and the resulting parameter estimates fully capture the pattern of supply and demand responses
underlying the cost and demand elastities necessary for evaluation and
interpretation of the impacts of markups, scale and utilization changes
on productive and financial performance.

Data and Estimation

Estimation of this model was carried out using U.S. manufacturing
data for 1952-1986 for a number of manufacturing industries. The sectors
considered include food and kindred products (FO), textiles (TX),
apparel and other textile products (AP), paper and allied products (PA),
printing and publishing (PP), chemicals and allied products (CM),
petroleum and coal products (PC), rubber and miscellaneous plastics
(RB), lumber and wood (LW), furniture and fixtures (FN), clay and glass
(CL), primary metals (PM), fabricated metal products (FM), machinery
(MC), electric and electronic equipment (EL), instruments and related
products (IN), and transportation equipment (TQ). In addition, a total
manufacturing category (MA), constructed by aggregating the individual
sectors using Divisia indexes, was estimated for comparison.

These data are based on series for prices and quantities of output
and inputs developed and used by the Bureau of Labor Statistics (BLS)
Office of Productivity.(7) The capital data were, however, reconstructed to generate an ex ante capital price measure more closely related to the
procedures used by Berndt and Wood |1~. Such a recalculation is required
because the "residual" method of capital measurement in the
BLS data generates an ex post measure of capital quasi-rents including
any returns not captured by other inputs. The demand variables were
primarily taken from the Economic Report of the President. The interest
rate used is the Moody Baa bond yield.

The model was estimated for each industry separately, using three
stage least squares to incorporate the endogeneity of output quantity
and price, and to allow for the possibility of non-static expectations
on input prices as suggested by Pindyck and Rotemberg |13~. The
instruments employed include lagged values of the exogenous variables facing the firm, as well as the world oil price, defense spending, and
the political party variables relied on in the Hall studies. The results
were quite robust to different specifications of instruments.

The estimated model for each of the manufacturing industries can be
used to generate a large number of indexes, elasticities, and other
parameter transformations. Since space constraints prohibit detailed
analysis of the different sectors, I concentrate here only on a general
evaluation of evidence on markups, scale economies and input fixity, and
their effects on productivity growth and economic profitability.(8)

Productivity Growth

Traditional multifactor productivity growth indexes
||Epsilon~.sub.Yt~ based on the K,L,E,M,S division of inputs are
presented in terms of average annual growth rates (AAGR) in Table I
(SICs for the industries are in parentheses).

The AAGRs reflect the existence of a post-1973 productivity growth
slowdown, even though the dramatic stagnation apparent immediately after
1973 in indexes representing yearly changes is somewhat masked by
including more recent years in the AAGR computations. The industries
which show a negative growth rate in the post-1973 period are PP, PM and
PC, the latter two of which are capital- and energy-intensive industries
which would tend to be heavily affected by energy price shocks. This
pattern is evident overall; the industries hardest hit in the mid-1970s
include PM, FM, MC, CM, PA, and RB, all of which are capital intensive.
These industries also, however, experienced relatively intense
international competition during this time period. The only industry
that exhibited increasing productivity growth was MC, which includes the
computer industry.(9)

The traditional productivity growth indexes appear considerably
procyclical, with, for example, declines appearing in most industries
around 1970, 1974-75 and 1982-83. One indication of the extent of these
fluctuations comes from the standard deviations of these measures, which
are rather large--particularly for durable goods industries.

The fluctuations observed, however, are less systematic than it might
initially appear, particularly given the emphasis on cyclicality in the
recent studies by Hall. The correlations of these indexes with indexes
reflecting cyclical trends are not very significant. In particular, when
this productivity growth measure is correlated with a standard published
capacity utilization measure (the Federal Reserve Board index for
manufacturing, FRB) or the C|U.sub.c~ measure resulting from estimation
of my model, the correlations tend to be primarily positive but
generally statistically insignificant.(10)

The cyclical fluctuations in productivity that do exist, although not
pervasive in terms of statistical significance, influence the
interpretation of changes in economic performance. Thus, it is useful to
see to what extent these variations might be smoothed, and in this sense
"explained", by taking into account cyclically related markup,
capacity utilization, and returns to scale factors.

TABULAR DATA OMITTED

These factors, and the associated adaptations of traditional
productivity growth measures, will now be considered in turn.

Markups

It has been argued that markups might be expected to be cyclical,
although controversy remains about whether they are pro- or
counter-cyclical.(11) Hall's treatment of the markup does not allow
for cyclicality to exist, since it is treated as a constant parameter.
However, the hypothesis of counteracting capacity utilization and
markups suggests that increasing markups would be accommodated by
additional excess capacity, leading to countercyclicality of markups, as
noted above. Domowitz, Hubbard and Peterson more directly address this
issue by correlating the markup measure with a published measure of
capacity utilization, and find some evidence of procyclicality. In the
current study, the cyclicality and determinants of the markup are
directly incorporated and thus can be more effectively evaluated.

The estimated markup indexes implied by my model are presented in
Table II in terms of annual averages. As found by Hall, significant
markups do appear to exist, although the estimates of the markups are
intuitively more reasonable than those based on the simpler framework of
the Hall studies.(12) The year-to-year variations are also important;
although the standard deviations are not large, clear tendencies do
emerge.

A secular increase in markups over time is evident (although indexes
specified in terms of yearly changes suggest significant year-to-year
variations). The only industries that exhibit a clear downward trend in
markups are AP, LW, PC and PM; this is consistent with intuition given
the intensifying international competition in the apparel, lumber and
primary metals markets, and the rise in costs of crude materials in the
petroleum refining industry which have caused downward pressure on
profit margins. Some other industries facing increasing international
competition such as CL and FM (and to a lesser extent TX and TQ) appear
from the averages to have quite stable TABULAR DATA OMITTED markup
behavior. Interestingly, markups in high-technology industries such as
CM, EL, MC and IN all increased from 1960-73 to 1973-86.

In general, markups appear to decline during recessions and in that
sense seem procyclical. For example for all industries the 1973 and 1979
OPEC shocks are reflected in a downturn in the markup ratio. However,
from correlations of the markup with the economic measure of capacity
utilization, C|U.sub.c~, the evidence is overwhelmingly in favor of countercyclicality of markups. The correlations of the reported markups
with C|U.sub.c~ (and the full cost elasticity ||Epsilon~.sub.CY~) are
negative throughout except for the primary metals industry (PM), and are
all statistically significant at the one percent level. For total
manufacturing (MA), for example, the correlation is -0.419 with a
standard error of .088. Correlations with published FRB capacity
utilization measures are somewhat more ambiguous; although the
correlations are generally negative, they tend to be small and largely
insignificant.

Countercyclicality of markups has a well defined impact on
productivity growth patterns through the error bias |Mathematical
Expression Omitted~. Since |Mathematical Expression Omitted~, and an
increase (in absolute value) in ||Epsilon~.sub.PY~ implies a larger
markup, an upward trend in the markup will compensate to some extent for
a downward trend in the productivity growth rate (as long as inputs in
general are increasing). Given the observed tendencies for increasing
markups and declining productivity growth, this provides a partial
"explanation" for measured downturns in productive
performance. More specifically, since this occurs for both secular and
cyclical fluctuations (markups are both increasing and countercyclical),
this implies that appropriate cost-based productivity growth measures
reveal stronger productive performance and less cyclicality in most
industries than standard primal measures.

Carrying out this correction for demand factors can, however, be
misleading if cost factors such as scale economies exist that should
also be accommodated in productivity growth measures, particularly given
the offsetting cyclical patterns of these market and technical forces.
Additional insights about fluctuations in traditionally measured
productivity growth can therefore be obtained by taking into account
also the impact of scale economies and fixity.

The Cost Elasticity, ||Epsilon~.sub.CY~, and Its Components

Fixity was incorporated in the Hall studies in the context of long
run returns to scale and the effect measured as a constant parameter. In
the model developed above, however, short and long run fixity--capacity
utilization and scale economies--are independently distinguished as
components of the cost elasticity ||Epsilon~.sub.CY~. This allows not
only measurement of the levels of these technological factors, but also
assessment of their trends, cyclical behavior, and impact on productive
and financial performance.

Capacity utilization is by definition procyclical; if output
increases, utilization of a given capacity increases. Similarly, if
scale economies exist, upward swings in the cycle (output expansion)
cause average cost declines, so this component of ||Epsilon~.sub.CY~
will also tend to be procyclical. This procyclicality suggests that
increased profitability from countercyclical markups will tend to be
offset by excess capacity and the existence of scale economies captured
in ||Epsilon~.sub.CY~.

The measured cost elasticity ||Epsilon~.sub.CY~ is presented in terms
of annual averages in the second panel of Table II. These measures
suggest short and long run scale economies exist and are quite
substantial in a number of industries. Scale economies also appear to be
increasing, especially in industries which tend to be more capital
intensive and have experienced productivity growth stagnation, such as
PA, CM, and PM.

One interesting exception to this is the MC industry. Although
productivity growth in this industry has been strong and actually
increasing, scale economies have also risen substantially. Note also
that this industry experienced one of the largest jumps in markups
during this period, as did CM, where scale economies also increased.
This is in sharp contrast to PM, where a (more modest) expansion of
scale economies occurred along with a decline in markups. This suggests
declining profitability as well as productivity performance in the
primary metals industry, due perhaps to a decline in relative efficiency
and increased international competition. To a lesser extent this is true
also for AP.

The procyclicality of the ||Epsilon~.sub.CY~ measure is more obvious
from indexes based on yearly changes, where, for example, declines are
evident for most industries in the downturns of 1969-70, 1974-75 and
1982-83. To a large extent cyclical movements in ||Epsilon~.sub.CY~ are
driven by utilization fluctuations, since potential scale economies
appear to be increasing over time rather smoothly. In turn, the capacity
utilization patterns appearing in the C|U.sub.c~ indexes result
primarily from changes in capital utilization, although labor hoarding,
and thus procyclicality from changes in work effort, are also evident
from fluctuations in the shadow value of labor.

The independent effects of short and long run fixities can be
distinguished from the two components TABULAR DATA OMITTED of
||Epsilon~.sub.CY~--C|U.sub.c~ and |Mathematical Expression Omitted~.
These measures are presented as annual averages in Table III, and
graphically for total manufacturing in Figure 1. The C|U.sub.c~ numbers
in Table III show that capacity utilization has been declining in every
industry but PC and LW. They also suggest excess capacity virtually
everywhere, although overutilization of capacity appears in the CM
industry throughout the time period, and in the early years for the
textile industry.

The excess capacity has been driven primarily, especially in the
post-1973 period, by a low shadow value of capital relative to its
market price; in most industries a decline in the |Z.sub.K~/|p.sub.K~
ratio and an increase in |Z.sub.L~/|p.sub.L~ has occurred post-1973.
Note also that the levels of C|U.sub.c~ are less than .9 in the PP, RB,
LW, FN, CL and PM industries in this time period, indicating that the
cost consequences of short-run excess capacity are often greater than
10%.

The bottom panel of Table III indicates, however, that scale
economies seem to be driving the evidence of a low and declining
||Epsilon~.sub.CY~ even more than C|U.sub.c~. In particular, long run
returns to scale (|Mathematical Expression Omitted~) are very
substantial and increasing, especially in the nondurable industries such
as TX, AP, PA and CM. Excess capacity therefore exists even in the long
run. Precisely why long-run scale economies are increasing over time in
all industries except CL and FM is a fascinating topic for further
research, since this result could reflect many different internal and
external scale factors.

Figure 1 shows graphically this balancing of |Mathematical Expression
Omitted~ and C|U.sub.c~ patterns in the observed cost elasticity
||Epsilon~.sub.CY~. Scale economies appear for manufacturing as a whole
to be quite large and increasing; |Mathematical Expression Omitted~ is
dropping. A more limited downward drift is evident from the capacity
utilization measure, as well as much more cyclicality.
||Epsilon~.sub.CY~ thus seems to reflect the cyclical fluctuations of
the utilization measure, and the level and secular trend of the
|Mathematical Expression Omitted~ measure.

The full effect of error bias corrections to accommodate the
deviation of ||Epsilon~.sub.CY~ from one is not immediately obvious a
priori, since the bias depends not only on this elasticity, but also on
the relative growth rates of output and quasi-fixed inputs. However, in
general procyclical variations in ||Epsilon~.sub.CY~ will result in
corrections incorporating ||Epsilon~.sub.CY~ |is not equal to~ 1 to
smooth the productivity growth measure and thus "explain" a
portion of observed secular and cyclical downturns, since procyclicality
implies greater output than input changes. These impacts are further
explored in the next subsection.

Productive Performance--Productivity Growth Corrected

The significant levels and trends of the measured markup, utilization
and scale measures discussed above suggest that adaptations to standard
productivity growth indexes to accommodate these effects will facilitate
interpretation of trends and fluctuations in these measures. Adapted
productivity growth measures incorporating these corrections are
presented in Table IV. The measure reported in the first panel of Table
IV is a primal-side measure recognizing the markup and error bias
corrections but including returns to scale and utilization as well as
technical change (|Mathematical Expression Omitted~), whereas that in
the second panel is a cost-side measure isolating the impact of
technical change (|Mathematical Expression Omitted~).

A comparison of the indexes in Tables I and IV indicate that
correcting for error biases resulting from markups and input fixity is
quantitatively important. In general productivity growth TABULAR DATA
OMITTED appears lower than reflected in the traditional measure for the
1960-73 period, but often is higher after 1973. Thus, the difference
between the pre- and post-1973 periods is substantially reduced and the
"productivity growth slowdown" somewhat attenuated.

For example, for total manufacturing, unadjusted growth rates for
1960-73 and 1973-86 are 1.610 and 0.489, while corresponding
fixity-adjusted values are 0.973 and 0.528. The entries in the first
panel of Table IV also suggest that efficiency growth in some industries
(including short and long run economies) has been very limited even from
the early years of the sample--especially in the PP, CM, PC, PM and IN
industries.

A further reduction in the apparent growth of technical change,
especially in the earlier part of the sample, is apparent in the second
panel of Table IV when the impacts of scale economies are removed; short
and long run scale effects have tended to bias technical change measures
upward, especially in earlier years when output growth was relatively
strong. However, in some industries, notably CL, PM and FN, standard
productivity growth measures have instead tended to understate technical
change. In addition, evidence of negative productivity growth is less
pervasive when scale impacts are recognized; some of the measured
productivity decline can be attributed to higher unit costs due to
diminished output demand.

In total, corrections to standard productivity growth measures
somewhat reduce secular and cyclical fluctuations in productivity growth
measures. This "smoothing" of the productivity growth index is
apparent from the year-to-year fluctuations summarized in the graph of
||Epsilon~.sub.Yt~ and |Mathematical Expression Omitted~ for total
manufacturing in Figure 2--especially for the strong upswings in the
early 1960s and closely following the downturns around 1970 and
1975.(13) The muting effect of the corrections is somewhat limited,
however, partly because some industries counteract the overall tendency
(the standard deviation for |Mathematical Expression Omitted~ is larger
than for ||Epsilon~.sub.Yt~ in some industries).(14)

Overall, corrections of productivity growth measures for error biases
due to erroneous assumptions about returns to scale and fixity provide
some insights into the "explanations" of productivity growth
fluctuations. However, it turns out that once these cost factors are
recognized, the correction of ||Epsilon~.sub.Yt~ for markups does not
significantly affect the evidence of productivity growth, because the
offsetting impacts of markups, utilization and scale imply approximately
normal profits and thus equivalence of cost and revenue shares. This is
developed in the next subsection.

Financial Performance--Profitability

The counteracting effects of markups and utilization/scale on
profitability are evident from the average annual levels of
|Mathematical Expression Omitted~ in Table V and Figure 3. ADJ TABULAR
DATA OMITTED tends to be close to one, suggesting that revenues
approximately equal economic costs, and that economic profits are
therefore roughly zero on average. Essentially, managers' pricing
responses balance the technical and market economic fluctuations
encountered, but do not allow for excess profitability on average.

The annual average ADJ measures presented in Table V suggest that
over time this balancing act has resulted in an increasing shortfall of
revenues over costs of production (including appropriate returns to
capital) in U.S. manufacturing industries. Although for total
manufacturing normal profits were approximated for the 1960 to 1986
period, a decline in profitability in the post-1973 period is evident
for all industries except PC. This trend exhibits little variation,
although some procyclicality appears to exist.

This downward trend in the ratio of returns to costs is evident from
Figure 3 for manufacturing overall. This Figure illustrates the
relatively greater impact on ADJ of the ||Epsilon~.sub.CY~ elasticity
than the markup ratio, since ADJ more closely follows the pattern
exhibited by the ||Epsilon~.sub.CY~ index. In particular,
||Epsilon~.sub.CY~ pulls down the ADJ measure over time; markups are not
keeping pace with changes in technical factors and competition. Thus,
even with greater potential for markups, expanding scale economies and
restrictions on flexibility due to capital fixity have had a depressing
effect on profitability for most U.S. manufacturing industries.

In particular, although before 1973 only six industries had negative
economic profits on average, post-1973 the number of such industries
more than doubled to thirteen. Only four industries experienced positive
economic profit in this later period (FO, PP, CM and PC), with FO and PC
the most profitable.

It is interesting to conjecture that these nondurable manufacturing
industries were perhaps subject to less intense competition than most of
the other industries during this period of massive international
expansion of markets. Other industries, even the MC industry which
performed better than other durable industries but still fell short of
normal profits by 1% on average, tended to be more internationally
competitive as well as more energy and capital intensive.

These numbers are dramatic confirmation of much recent discussion
about declining competitiveness of U.S. durable goods and textiles
industries. It should be noted, however, that the post-1973 decline in
profitability was reversing toward the end of this sample; yearly
indexes show increasing profitability after 1982, with positive economic
profits by the end of the sample for the MC industry. It will be useful
to explore this trend further with the availability of more recent data.

This evidence about financial performance, as noted in the previous
subsection, provides some insights about the linkage between measures of
productive and financial performance. The Hall markup correction to
measure input shares in terms of costs instead of revenues will have
little impact on average, since ADJ closely approximates one. However,
some pattern in the difference between cost and revenue shares is
implied by the reduction in profitability over time; a measure based on
cost shares will tend to show a somewhat smaller decline in productivity
growth over time.

IV. Concluding Remarks

This paper addresses some determinants of productive and financial
performance using a structural model allowing formalization and
measurement of the relationships among productivity growth, profits,
markup behavior, capacity utilization and scale economies. This
framework has permitted consideration of whether these market and
technical factors generally ignored in productivity growth analysis have
been "responsible" for cyclical fluctuations and secular
downturns in economic performance observed in U.S. manufacturing
industries.

The first "cause" evaluated is the markup of price over
marginal cost. Markup indexes embodying a cyclical component constructed
for these industries reveal tendencies for markups to increase over time
and in cyclical downturns (implying countercyclicality). As a result,
traditional primal productivity growth measures, developed in terms of
revenue shares and thus implicitly based on the assumption of perfect
competition, exacerbate declines over time and in recessionary periods.
Adaptation of the measure to reflect cost shares therefore provides some
"explanatory power" for productivity performance variation, by
smoothing observed fluctuations.

However, fixities in both the short and long run also have an impact
on observed economic performance. In the model used here, short run
fixities are captured as changes in capacity utilization, and long run
"fixities" are reflected as scale economies. Although capacity
utilization is by definition procyclical, I find it also appears to have
a downward secular trend. At the same time, the extent of scale
economies seems to be increasing over time. This is consistent with
economic intuition, for in order to obtain normal economic profits,
increasing markups must be offset by a combination of increasing excess
capacity and scale economies. The empirical results confirm this
counteracting effect in U.S. manufacturing industries; economic profits
on average have been zero, but have exhibited a downward trend over time
as scale economies have more than outweighed rising markups.

Together, these forces tend to offset the explanatory power of
adjustments of primal productivity growth measures for markups. However,
incorporating the cost characteristics--utilization and scale--still
contributes in an important way to "explaining" fluctuations
in productivity growth in terms of error biases. Corrections of
erroneous assumptions made in traditional computations have a limited
but significant smoothing impact on observed trends in productivity
growth and technical change.

1. see Ohta |12~ or Morrison |11~ for further elaboration of this
equality.

2. Clearly other internal and external factors such as R&D
expenditures or infrastructure capital not appropriately reflected in
these measures also will affect this relationship. Only these three
determinants of the deviation will, however, be taken into account here.

4. A somewhat different argument for countercyclical markups,
motivated by industrial organization theory, has been presented by
Rotemberg and Saloner |15~.

5. See Morrison |10~ for further elaboration of this relationship and
the following adaptations.

6. For further details of the model and its application in the
current context, see Morrison |6;8~.

7. The data, including detailed data for the capital components, were
graciously provided by Michael Harper.

8. The interested reader can pursue the analysis further using the
yearly indexes presented in Morrison |8~. The results in the text are
presented for all industries in terms of average annual growth rates
calculated from the relevant indexes. Computations of most measures
referred to in the next subsections can be made directly from the
indexes in Morrison |8~. Other results, such as the shadow value ratios
underlying the C|U.sub.c~ measures, require further computation.

9. Semiconductors are included in EL, which also experienced very
strong productivity growth over this period, particularly in the late
1970s. The relatively strong performance of the MC industry is driven
largely by an enormous productivity growth rate in 1984-86.

10. For more details about the correlation patterns in these
measures, see Morrison |8~.

11. See Morrison |7;9~ for further elaboration of the cyclicality of
markups and its determinants.

12. This is particularly true for the CM, FO, PC and PP industries,
for which the Hall estimates are clear outliers (with markup ratios of
20.112, 5.291, - 139.478 and 14.263, respectively).

13. Only these two indexes are graphed since |Mathematical Expression
Omitted~ and |Mathematical Expression Omitted~ are so similar that they
tend to overlap.

14. This smoothing is also evident from correlations of the corrected
productivity residuals with utilization indexes, which are not as
statistically significant as those for the standard measures.

References

1. Berndt, Ernst R., and David O. Wood. "Energy Price Changes
and the Induced Revaluation of Durable Capital in U.S. Manufacturing
During the OPEC Decade." Manuscript, M.I.T. Center for Energy
Policy Research, January 1984.